Ibrahimovic added gloss to the scoreline with his second of the night in injury time.
United manager Mourinho was not seen inside the arena after accepting a touchline ban earlier in the day for his sending-off during Sunday's Premier League clash between the same two sides.
From wherever the Portuguese chose to watch, he will presumably have been pleased with his side's high-energy and clinical performance.
The only disappointment for United fans was the failure of captain Wayne Rooney to score the goal that would have equalled Sir Bobby Charlton's club record on his return to the starting line-up.
That will now have to wait a little longer as a booking for dissent means Rooney will be suspended for this weekend's trip to Everton.
The supporters did at least get to welcome Bastian Schweinsteiger back to the pitch after his long exile with a late substitute cameo.
United conceded after just 90 seconds against West Ham on Sunday but roles were reversed this time as the hosts made a blistering start and swept into a second-minute lead.
Rooney found Henrikh Mkhitaryan in space with a good touch and the rejuvenated Armenian presented Ibrahimovic with an inviting opportunity with a neat backheel. The Swede showed great composure as he calmly dinked the ball over the advancing Adrian for his 10th United goal.
Ibrahimovic took a blow for his troubles as Adrian caught him with his studs in his follow-through and the goalkeeper might have been lucky to escape punishment.
Ibrahimovic had another shot blocked by Winston Reid and two rapid United counter-attacks ended with Martial first being felled just outside the area and then blasting over. Rooney forced Adrian to palm wide from a curling free-kick.
The Hammers offered little until equalising against the run of play 10 minutes before the interval. David de Gea was at fault as he failed to hold a long-range Dimitri Payet strike and United academy product Fletcher snaffled his chance. The 21-year-old, who left the Red Devils in the summer, did not overdo his celebrations but punched the air in delight.
United picked their game up again after the break, reclaiming their lead after 48 minutes as Mkhitaryan squared for Martial to sweep home his first.
The Frenchman added another to make the game safe just after the hour, this time with a simple finish at the end of a slick move involving Ibrahimovic and Antonio Valencia.
Rooney had been influential throughout but at this point he noticeably moved up a gear as he chased his landmark goal.
He showed some of his aggression as he won possession and curled a shot wide. He suffered a cut cheek after being kicked in the face by Reid in another attack but that only seemed to fire him up more.
It was not to be for him on this occasion, however, with Ibrahimovic tapping home the fourth late on.
Schweinsteiger returns from exile
Bastian Schweinsteiger returned from his Manchester United exile with a late substitute appearance in Wednesday's EFL Cup quarter-final against West Ham.
The German World Cup winner, who was frozen out of the first-team picture and forced to train alone earlier in the season, came off the bench for the last four minutes as United won 4-1 at Old Trafford.
The 32-year-old was an unused substitute for Sunday's Premier League draw against the Hammers, his first appearance in a matchday squad since Jose Mourinho took over as manager in the summer.
EFL Cup can offer Jose Mourinho the salvation he needs
There was a time in Liverpool’s pomp when they called the League Cup the Mickey Mouse Cup, so breezily did they view it, but those with long memories at Manchester United have a different view of it, based on the events of a decade ago.
In the winter of the 2005/06 season the club, when the club were struggling to come to terms with the swagger of Jose Mourinho’s newly-monied Chelsea, Sir Alex Ferguson suddenly stopped fielding his reserves in the competition and began to view it as an opportunity to win something and bring some pride back. “It’s a great competition,” he said after Blackburn Rovers had been despatched in the semi-final that year. “The Carling Cup represents a great opportunity to mark the season as a successful one. I’m delighted to be in the final.”
One fans website at the time described the competition as “a $50 hooker compared to the supermodels we used to date”, but when United beat Wigan Athletic 4-0 in the final, the shackles were lifted. It was the launch-pad to a renewed period of United dominance.
The situation is similar on Wednesday night, as the side go back into battle against West Ham United, after a 1-1 draw at Old Trafford on Sunday which left the side with statistically their worst start to a league season for 27 years with just 20 points from 13 games.
Though meaningful title discussions cannot be had in late November, the notion of Jose Mourinho strolling into Manchester and immediately clinching the big domestic prize seems already to be remote. This competition could offer salvation and though the presence of Liverpool in the semi-finals presents an obstacle, United could find a way to get a winning habit back. They will fear neither Hull City, who have also progressed, and both Arsenal and Southampton, who contest the other quarter, seem beatable.
United will be without midfielder Paul Pogba, who collected his fifth booking of the season on Sunday in the incident which led to Mourinho being sent to the stands for the second time this season. Yet when the side last ventured into EFL Cup action under a cloud – at Northampton Town, on the back of defeats to Watford and Manchester City – it provided an opportunity for the players who had found themselves excluded. Michael Carrick and Ander Herrera were both excellent that night.
The suspension of Marouane Fellaini, as well as Pogba, could actually open the door for Bastian Schweinsteiger on Wednesday, after he was recalled to the bench at the weekend. Wayne Rooney can also expect a starting role and as he is now one goal short of equalling Sir Bobby Charlton's club record goal tally of 249, the game presents another chance to remind United of their status and the greats who have gone before.
In the background details of the final against Wigan in 2006 there are reminders of the storms that can hover over a club of United’s status and yet soon pass on. The pre-match press conference saw The Times barred because Sir Alex Ferguson was offended by them questioning why the club had paid £7.2m for Nemanja Vidic. Ancient history now and Mourinho knows that lifting this trophy can do the same for Old Trafford a decade on.
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